# Homework Help: Balancing forces on a particle

1. Aug 15, 2013

### Final_HB

1. The problem statement, all variables and given/known data
A particle is under the influence of 5 forces. Three of these forces are reversed, and the particle remains in equilibrium. Prove that the particle will remain in equilibrium even if these three forces were removed altogether.

3. The attempt at a solution
My thinking for this is:
With three of the forces gone, the 2 forces (F1 and F2 ) left must balance the system if its to remain at equilibrium.
If change of forces occurs, the system will react by moving to a new state of equilibrium.
No reaction means that the 3 forces in the question cancel out each other, and no shift occurs.
If the three forces balance to 0, there is no need to have them as acting on the particle.

Right?

If im right, Is there any maths way to say this, or a better way to explain what im trying to say. Thank you in advance.

2. Aug 15, 2013

### ehild

You are right, but it can be formulated mathematically. Write up the sum of forces for both cases, and manipulate the equations.

ehild

3. Aug 15, 2013

### Final_HB

Well...

F1+F2+F3+F4+F5=0

And for the second:
F1+F2-F3-F4-F5=0

taking one away from the other gives us:
2F1+2F2=0
So,
F1+F2=0

4. Aug 15, 2013

### ehild

If you mean subtract " by taking one away from the other" the result is 2(F3+F4+F5)=0, so the resultant of these three forces is zero, they can be omitted. And then F1+F2=0, too.

ehild